(Received 25 August 2010; published 7 January 2011)Superhydrophobic (SHPo) surfaces have shown promise for passive drag reduction because theirsurface structures can hold a lubricating gas ﬁlm between the solid surface and the liquid in contact with it.However, the types of SHPo surfaces that would produce any meaningful amount of reduction get wetunder liquid pressure or at surface defects, both of which are unavoidable in the real world. In this Letter,we solve the above problem by (1) discovering surface structures that allow the restoration of a gas blanketfrom a wetted state while fully immersed underwater and (2) devising a self-controlled gas-generationmechanism that maintains the SHPo condition under high liquid pressures (tested up to 7 atm) as well as inthe presence of surface defects, thus removing a fundamental barrier against the implementation of SHPosurfaces for drag reduction.

Recently, structured hydrophobic surfaces exhibitingsuperhydrophobicity have shown promise as gas-lubricated surfaces because their surface structures canhold a gas ﬁlm when submerged in a liquid [1–8][Fig.1(a)]. Some have even demonstrated effective sliplengths [9] up to hundreds of micrometers [6,7], which arelarge enough to beneﬁt regular (i.e., large) ﬂuidic systems.Drag reduction for turbulent ﬂows has also been reported[8]. Superhydrophobic (SHPo) surfaces are considered asuperior alternative to the existing bubble injection method[10] for drag reduction because the stable gas upon thesurfaces makes the SHPo method passive (i.e., energyefﬁcient) and simple (i.e., easy to implement). Moreover,it has been shown that the minimized solid-liquid contacton SHPo surfaces can resist surface fouling [11]. Despiteits great potential, drag reduction by SHPo surfaces hasbeen considered strictly limited to laboratory conditionsbecause of one main unanswered question: Can they retainthe gas under real conditions? This problem is ratherfundamental and should be addressed ﬁrst, so that morepractical issues like biofouling and cost are even relevant.Because the wetting transition of a SHPo surface is spon-taneous, any liquid impregnation, incited by variousinstigators [12,13], has an irrevocable effect against dragreduction, as illustrated in Figs.1(a)and1(c). For example,the surface may get wet and lose its slip effect if it hasdefects, the liquid is under pressure [12], or thegas diffusesaway over time [13].Recently, several approaches have been suggestedto increase the stability of the gas layer on a SHPosurface against liquid pressure [7,14,15]: e.g., nanostruc-turing the sidewall of the microstructures [7] and pressur-izing the gas layer [14,15]. However, these approaches areonly preventive measures. They are ineffective once thegas layer is disrupted. The ability to restore underwatersuperhydrophobicity even after the surface structures be-come wetted is more desirable. A successful schemeshould be able to displace the liquid that has impregnatedthe surface structures with new gas and reform a stable gasﬁlm, as illustrated in Fig.1(d). Note the recovery of theSHPo state shown for sessile droplets surrounded by air[16,17] is not helpful for drag reduction, which pertains tothe entire surface being fully immersed underwater.To restore a stable gas layer, we reason that the new gasshould not grow vertically off the surface structures beforespreading laterally between them. We propose that thisgoal can be achieved by designing the surface structuresto satisfy a certain geometric criterion, given belowfor post structures (see supplementary material fordetails [18], which addresses the case of grate structuresas well):

refer to the surface of the posts and the bottomsurface between the posts, respectively. The upper boundvalue of

H=L

shown in Eq. (1) was derived from a geo-metric requirement that the gas should grow with lessresistance in the lateral direction than in the vertical direc-tion. The maximum gas pressure the interfaces can sus-tain against vertical (i.e., undesirable) growth is

Á

P

v

¼ð

D

sin



p;

rec

Þ

=L

2



, while the minimum pressure neededto sustain the lateral growth (i.e., the two vertical contactlines on the sidewall of a post merge and depart from thewall) is

Á

P

l

¼ð

L

cos



b;

rec

þ

2

H

sin



p;

rec

Þ

=HL

. The ﬁrstand second term represent the resistance by the bottomsurface and that by the post sidewall, respectively. For thebubble to grow laterally without vertical outgrowth, thegaspressure should be higher than

Á

P

l

but lower than

Á

P

v

,providing a qualitative guideline for the design of SHPosurfaces that allow the restoration of a stable gas layer. Thelower bound value of

H=L

in Eq. (1) was derived fromanother geometric requirement that, once the gas ﬁlm isformed, the liquid-gas meniscus should not touch the bot-tom surface as a result of the liquid pressure, on thecondition that the height of the posts should be greaterthan the maximum sagging depth of the meniscus [2].When

CA

rec

on the bottom surface is 110



, correspond-ing to a smooth surface of a highly hydrophobic material(e.g., Teﬂon

Ò

), there is only a limited regime that satisﬁesthe right-hand side of Eq. (1) [Fig.2(a)]. In order toincrease this

CA

b;

rec

further, expanding the regime of satisfactory values,wepropose tonanostructurethebottomsurface and render it a solid-gas composite. According tothe Cassie-Baxter equation [19],

cos



c

¼



þð

1

À



Þ

cos

;

(2)where



isthe intrinsicCA ona smoothsurfaceand



c

istheapparent CA on the nanostructured surface.



¼

110



,



c

can be increased to 173.4



by employing nanostructureswith a gas fraction of 0.99. Accordingly, the geometricregime of posts that satisfy Eq. (1) is signiﬁcantly expandedif the bottom surface is nanostructured [Fig.2(a)]. Thisapproach is schematically represented in Fig.2(b). Whenthe microstructures become wetted, a residual gas remainsin between the nanostructures due to their high resistanceagainst liquid impalement, keeping the bottom surfaceSHPo. When there is an inﬂux of gas, the large contactangle on the SHPo bottom surface helps the gas spread pastthe posts laterally and recover the gas layer among themicrostructures.Based on the aforementioned geometrical requirementsfor successful gas spreading, hydrophobic microstructureswere constructed on a substrate surface covered in hydro-phobic nanostructures, as shown in Fig.2(c). To fabricatesuch hierarchical SHPo surfaces, nanostructures wereformed on a 4 in. silicon wafer using a black siliconmethod, on which a gas fraction over 99% and contactangle over 175

) that allows formation of a gas ﬁlm betweenposts as function of their gas fraction with

CA

b;

rec

as a parameter.Red line represents the minimum

H=L

and black line themaximum

H=L

acceptable, following Eq. (1). Microposts of varying gas fraction and pitch (while height is ﬁxed at

50



m

),denoted with

d

, have been fabricated on both smooth andnanostructured bottom surfaces and tested. The gas ﬁlm resto-ration was achieved only when the acceptable zone was ex-panded due to the increased

CA

rec

on the nanostructured bottomsurface, qualitatively agreeing with the theory. (b) Schematicrepresentation of the successful gas ﬁlm formation. (c) Scanningelectron microscopy images of a test surface fabricated based onthe above criteria.

PRL

106,

014502 (2011)PHYSICAL REVIEW LETTERS

week ending7 JANUARY 2011

014502-2

electrolysis on the bottom surface,

50



m

-thick negativephotoresist (KMPR1050, Microchem) was spin coated onthe wafer, and microstructures (posts or grates) with vary-ing pitches and gas fractions were patterned out of thephotoresist. Finally, to make all the surfaces hydrophobic,2 wt% Teﬂon

Ò

AF solution (Dupont) was spin coated.To replenish the gas layer lost upon wetting, electrolysiswas deemed better suited than other gas-generation meth-ods such as thermal, pneumatic, and chemical on accountof its low power consumption [20], the stability of thegenerated gases [21], its easy integration into a system,and its compatibility with water. In this study, we used aline pattern of thin-ﬁlm gold on the bottom surface as thecathode [Fig.2(c)] and a copper wire in the water as theanode to perform electrolysis. The placement of the elec-trodes on the bottom surface imposes a self-controlled (i.e.,self-activating and self-limiting) generation of gas becausethe electrolytic circuit closes, starting gas generation, onlywhen and where the microstructures become wetted (i.e.,the liquid touches the cathode), and opens, halting the gasgeneration, as soon as the dewetting is complete.A series of experiments were conducted to verify theeffectiveness of the proposed scheme by restoring under-water superhydrophobicity under the worst-case scenarioof all the microstructures being wet. Before applying anyvoltage, the water tank was ﬁrst subjected to a moderatevacuum (1–2 kPa), which made all the microstructures wetbut not the nanostructures. After the wetting was con-ﬁrmed,weapplied10Vbetweenthecathodeonthesampleand the anodewire 1 cm above the sample inside thewater,starting electrolysis. As a reference, we prepared a controlsurface having microposts on a smooth bottom surface[Fig.3(a)]. In this case, the generated gas tended to pro-duce several individual bubbles, which protruded over thetop of the posts rather than forming a ﬁlm, failing to coverthe surface evenly (see video S1 in [18]). For the proposedsurface having microposts on a nanostructured bottom[Figs.3(b)and3(c)], in comparison, a nonwetted areawas gradually recovered as the gas ﬁlm spread withoutprotruding over the microposts. The entire test area(

2 cm

Â

2 cm

) became dewetted after several minutes(see videos S2 and S3 in [18]). A schematic illustrationof bubble generation on the wetted surface of microposts isshown in Fig. S6 in [18] along with the test setup.A dewetting process begins with patches of gas ﬁlmappearing at random locations in a wetted area. Afterthat, the growth of gas occurs mainly via Oswald ripening[22], since the gas is interconnected everywhere viathe thin residual layer on the bottom surface between thenanostructures. In Oswald ripening, the gas inside thesmaller bubbles is transported to the larger bubbles (i.e.,a gas ﬁlm) due to the difference in Laplace pressures,leading to the continuous growth of a large gas ﬁlm untilthe gas ﬁlm covers the whole area. The current approachwas also applied to regenerate a gas layer on a surface of grating microstructures as well, as shown in Fig.3(d)andvideo S4 in [18].The total power consumption needed for complete res-torationof thegas ﬁlm onthe testarea of

2 cm

Â

2 cm

wasestimated to be about 6 mW for 150 sec. This value, whilemuch larger than the inherent power requirement due tothe Teﬂon

Ò

layer covering the electrodes and the accom-panying components in the test setup, is nonethelessmuch smaller than that needed for a thermal method(e.g., 1–100 W [20]). It is worth noting that the presenceof nanostructures on the bottom surface offers anotheradvantage for practical applications. When a liquid im-pregnates microstructures on a smooth bottom surface, thewetting tends to spread rapidly to the surrounding area,leading to a cascade of wetting over the entire area [6]. Incontrast,withthebottomsurfacenanostructuredand super-hydrophobic in its own right against liquid pressure, oursurfaces conﬁne the wetting to limited regions and resistfurther liquid spreading. This feature helps restore a gaslayer on microstructures with surface defects [23].Another important implication of our surface for prac-tical applications is that our surface can retain a stable gaslayer even under high liquid pressure. An electrolyticallygenerated gas automatically adjusts its pressure to that of the liquid, such that a gas layer on our surface can effec-tively resist high liquid pressure. We experimentally veri-ﬁed that a gas layer can be retained on our surface underpressurized liquid (tested up to 7 atm) by employing thecurrent gas restoration scheme. This feature can signiﬁ-cantly expand the applicability of a SHPo surface to a